This classic introduction to the main areas ofmathematical logic provides the basis for a firstgraduate course in the subject. It embodies the viewpointthat mathematical logic is not a collection of vaguelyrelated results, but a coherent method of attacking someof the most interesting problems, which face themathematician. The author presents the basic concepts inan unusually clear and accessible fashion, concentratingon what he views as the central topics of mathematicallogic: proof theory, model theory, recursion theory,axiomatic number theory, and set theory. There are manyexercises, and they provide the outline of what amountsto a second book that goes into all topics in more depth.This book has played a role in the education of manymature and accomplished researchers.